Question

X Company is considering a new processor that costs $150,000. Shipping and setup costs for the new processor are estimated to be $15,000. X’s working capital requirement is expected to increase by $17,000 when the new processor begins operation and is expected to be fully recoverable at the end of the project. The new processor’s useful life is expected to be 5 years and its salvage value at that point is estimated to be $60,000. The new processor is being depreciated using a 5-year ACRS life. Assume a tax rate of 35% and a cost of capital of 12%. Estimated incremental revenues and incremental cash operating expenses for the new processor before tax for each year are shown in the table below.

Year	Incremental Revenue	Incremental Cash Operating Expenses	ACRS Depr. %
1	$87,000	$23,000	15
2	$82,000	$25,000	22
3	$93,000	$30,000	21
4	$87,000	$23,000	21
5	$88,000	$29,000	21

Q1. What is the cost of the initial outlay?

Q2. Given the initial outlay for the new processor, assume the following yearly incremental after-tax cash flows (below) . Assume a cost of capital of 12%. What is the NPV of the Project?

Year 1	$40,000
Year 2	$40,000
Year 3	$50,000
Year 4	$55,000
Year 5	$100,000

Q3. Given the initial outlay for the new processor, assume the following yearly incremental cash flows (below). Assume a cost of capital of 12%. What is the IRR of the Project?

Year 1	$45,000
Year 2	$45,000
Year 3	$50,000
Year 4	$50,000
Year 5	$105,000

Answer 1

Q1. Cost of initial outlay = Cost of new processor + shipping and setup costs + increase in working capital

Cost of initial outlay = $150,000 + $15,000 + $17,000 = $182,000

Q2. NPV = sum of present value of incremental after-tax cash flows - Cost of initial outlay

sum of present value of incremental after-tax cash flows = Year 1 incremental after-tax cash flow/(1+cost of capital) + Year 2 incremental after-tax cash flow/(1+cost of capital)² ... + Year 5 incremental after-tax cash flow/(1+cost of capital)⁵

Years	Cash flows
0	-$182,000
1	$40,000
2	$40,000
3	$50,000
4	$55,000
5	$100,000
Cost of capital	12%
NPV	$12,887.23

Calculation

Q3. IRR is the internal rate of return at which present value of incremental after-tax cash flows is equal to Cost of initial outlay

Cost of initial outlay = Year 1 incremental after-tax cash flow/(1+IRR) + Year 2 incremental after-tax cash flow/(1+IRR)² ... + Year 5 incremental after-tax cash flow/(1+IRR)⁵

Years	Cash flows
0	-$182,000
1	$45,000
2	$45,000
3	$50,000
4	$50,000
5	$105,000
IRR	15.97%

Calculation